chemical physics of discharges - Argonne National Laboratory

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The remarkable aspect of this result comes on the insertion of numbers in
Eq. (17). If for example, one has electrons moving through a gas with M 30 AMU,
at pressures giving X ?r Imm (i.e. p 6 1 torr) then the mean energy in ev is around
25 times the field strength in volts/cm. With as little as a few tenths of v/cm
fields, mean electron energies are several ev. We can thus understmd the appearance
of high electron "tempreatures" in gas discharges.
It is beyond the scope of this review to go further and question the distribution ,
of electrcn energies. It is sufficient to indicate that if one takes assumptions
similar to those nade in this simplified argument and utilizes them in the Boltzmann
ea-uation, one can obtain an approximate solution for the distribution of speeds. The t
result is not the I.laxwell-Boltzmann distribution, but rather that known as the
Druyvesteyn distribution whose dependence on speed is given by
This distribution function is similar in shape to the hxwell-Boltzmann distribution
for a given mean speed, except that the most prob2ble speed is slightly higher and the
high energy tail is diminished in the Druyvesteyn distribution. Nonetheless, the
distributions are sufficiently similar that one can, to good approximation, think of
the electrons as having a temperature in the Maxwellian sense which is much higher than
the neutral gas temperature; i.e. typically 30,000'K vs 300'K. It is this dichotomy of
temperatures which is perhaps the most striking of the non-equilibrium aspects of a gas
discharge.
This general effect of collisions randomizing the direction of motion of electrons
which have picked up energy from the field between collisions has another important
manifestation. It is responsible for the operation of microwave electrodeless
discharges.
E(t) = Eo cos ut, then Newton's law for the electron becomes, in the absence of
collisions,
which solves to give
If we consider an electron moving in an ac field which is of the form
The rate of energy pickup from the field i.e. the power, P is given by
tEv
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